This book has a fundamental relationship to the International Seminar on
Fuzzy Set Theory held each September in Linz, Austria. First, this
volume is an extended account of the eleventh Seminar of 1989. Second,
and more importantly, it is the culmination of the tradition of the
preceding ten Seminars. The purpose of the Linz Seminar, since its
inception, was and is to foster the development of the mathematical
aspects of fuzzy sets. In the earlier years, this was accomplished by
bringing together for a week small grou ps of mathematicians in various
fields in an intimate, focused environment which promoted much informal,
critical discussion in addition to formal presentations. Beginning with
the tenth Seminar, the intimate setting was retained, but each Seminar
narrowed in theme; and participation was broadened to include both
younger scholars within, and established mathematicians outside, the
mathematical mainstream of fuzzy sets theory. Most of the material of
this book was developed over the years in close association with the
Seminar or influenced by what transpired at Linz. For much of the
content, it played a crucial role in either stimulating this material or
in providing feedback and the necessary screening of ideas. Thus we may
fairly say that the book, and the eleventh Seminar to which it is
directly related, are in many respects a culmination of the previous
Seminars.